非对称随机重置：灾难性事件建模
Asymmetric Stochastic Resetting: Modeling Catastrophic Events
摘要：
在经典的随机重置问题中，一个粒子，根据一些随机动力学运动，经历随机中断，使它到一个选定的区域，然后，该过程重新开始。目前，重置机制已被引入作为关于优选位置的对称重置。然而，在本质上，存在系统只能从某些方向重置的若干实例，例如，灾难性事件受此启发，我们考虑正实数线上的连续随机过程。该过程在以恒定速率发生的随机时间被中断，然后，只有当当前值超过阈值时，前者才重新定位到一个值;否则，它遵循底层过程定义的轨迹而不重置。我们提出了一个一般的框架，以获得精确的非平衡系统的定态和系统到达原点的平均第一通过时间。利用这个框架，我们得到了两个不同模型系统的显式解。一些经典的结果发现对称复位，如存在一个最佳复位，强烈修改。最后，进行了数值模拟，以验证分析结果，显示出良好的协议。
英文摘要：
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism has been introduced as a symmetric reset about the preferred location. However, in nature, there are several instances where a system can only reset from certain directions, e.g., catastrophic events. Motivated by this, we consider a continuous stochastic process on the positive real line. The process is interrupted at random times occurring at a constant rate, and then, the former relocates to a value only if the current one exceeds a threshold; otherwise, it follows the trajectory defined by the underlying process without resetting. We present a general framework to obtain the exact non-equilibrium steady state of the system and the mean first passage time for the system to reach the origin. Employing this framework, we obtain the explicit solutions for two different model systems. Some of the classical results found in symmetric resetting such as the existence of an optimal resetting, are strongly modified. Finally, numerical simulations have been performed to verify the analytical findings, showing an excellent agreement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
